Extended  semilocal convergence for the Newton- Kurchatov method

H.P. Yarmola; I. K. Argyros; S.M. Shakhno

doi:10.30970/ms.53.1.85-91

H.P. Yarmola Department of Computational Mathematics, Ivan Franko National University of Lviv, Lviv, Ukraine
I. K. Argyros Department of Mathematics, Cameron University, Lawton, USA
S.M. Shakhno Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, Lviv, Ukraine

DOI: https://doi.org/10.30970/ms.53.1.85-91

Keywords: Nonlinear equation; Newton-Kurchatov method; Semilocal convergence; Decomposition of operator

Abstract

We provide a semilocal analysis of the Newton-Kurchatov method for solving nonlinear equations involving a splitting of an operator. Iterative methods have a limited restricted region in general. A convergence of this method is presented under classical Lipschitz conditions.
The novelty of our paper lies in the fact that we obtain weaker sufficient semilocal convergence criteria and tighter error estimates than in earlier works. We find a more precise location than before where the iterates lie resulting to at least as small Lipschitz constants. Moreover, no additional computations are needed than before. Finally, we give results of numerical experiments.

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